Bill and List: To quote Boss Caine in "Cool Hand Luke", "what we have heah is a failyuh to communicate." First, I am uncomfortable with the word temperament here, because the intervals are fixed in one dimension, and cannot be tempered. The only intervals that can be tempered are those among the open strings. I don't think you [Bill] have answered my one central problem. Let me try to state it another way. In any temperament system on a single-voiced keyboard intrument, once you have set a temperament, every occurrance of a given note, let us use A as an example, is tuned to the A in the temperament octave, except for a little stretching. There is only one key, integer, which locates a given pitch. On a guitar, a cartesian co-ordinate system locates the pitches, with strings along the y axis and frets along the x axis. and there are several solutions for all but the lowest and highest notes; that is, I can produce the (theoretically)identical pitch using several different fret/string combinations. I attempted to show that for 1 solution in each case, the result would be an intolerable octave. But even if it is not intolerable, the point is that in any given temperament on a keyboard the same interval (say A-C#) has the same character or colour, in any register, and that cannot hold true on a guitar. On the contrary, all *parallel* intervals formed by moving that shape up the neck on the same pair of strings will have the same character (A#-D, B-D#, C-E# etc) whereas the interval A-C# will have a *different* character using any other combination of strings and frets. >I must respectfully say that there is > something wrong with your conclusions. I must respectfully ask you to tell me what that might be. >If you claim that what I hypothesized "wouldn't work" > then you would have to say that whatever you do "wouldn't work" either. No, I just claim that a different "temperament" is required for most keys. > I did not comment on the other styles of tuning you mentioned because they did > not involve the issue of ET vs. WT. I have observed that many people tune > their guitars by making solid unisons with a fret and open string as you > describe. On the contrary, I think you must have misunderstood what I was talking about. An open tuning is one in which all the strings on the guitar form a chord when played unstopped, or "open". Temperament is most certainly relevant to open tunings, and non-equal temperaments are probably particularly apt, because there are fewer different chord voicings used--mostly single note or double-stopped melody lines within a more or less fixed harmonic framework. > > If you do not have an SAT and would like to approximate the 1/6 comma ditonic > WT by ear, here is how you would do it: I will certainly try it. Never let it be said that I don't have an open mind. Tim Keenan Terrace, BC
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